For now, the largest threat to the two companies comes from the developing world, where brands unknown in the West are quickly devouring Apple and Samsung’s business, thanks to lower prices.

Fitch says Apple risks losing a fifth of its global market share within a year, falling to 25 per cent of smartphone sales from 31 per cent in 2013.

Samsung could see its market share drop a notch as well, to 14 per cent from 15 per cent, Fitch predicted.

“We expect the big two's combined smartphone shipment volume to stagnate at around 450 million-460 million units in 2014 [down from 467 million in 2013], even as the global smartphone market rises by around 20 per cent to 1.2 billion,” Fitch said.

Much of the growth in the smartphone market will come from the developing world because developed markets are saturated at this point, Fitch said. China and India will account for 60 per cent of global growth in smartphone sales.

"Local handset makers including China's Xiaomi, Lenovo, Huawei and India's Micromax Informatics are the principal large competitors for Apple and Samsung," Fitch wrote. These competitors are selling phones in the $100-to-$300 U.S. range, while Apple and Samsung phones retail for closer to $600, without carrier subsidies.

In developed countries, profitability is falling for smartphone makers because there is little room for growth and competitors are making cheaper phones and undercutting the big players, Fitch said.

Apple is expected to release the iPhone 6 in September, but Fitch doesn’t believe it will halt the company’s decline.

“Developments are likely to be incremental rather than revolutionary,” Fitch wrote. “We believe that the innovations — which include curved screens and compatible wearable devices — are unlikely to change the trend facing Samsung and Apple.”

Apple shares were up about 0.3 per cent on the NASDAQ Tuesday mid-day, despite the report. Apple shares are up about 30 per cent since the start of the year, while Samsung shares are flat year-to-date.

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12 Contradictory iPhone 6 Rumour Videos

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"Apple's iPhone 6 was expected to hit stores in September, but the rumor mill is now pointing to an even earlier release date.:

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